Patient satisfaction. Source: Neter  Problem 6.15

A hospital administrator wished to study the relation between 
patient satisfaction (Y) and patient's age (Xl, in years), 
severity of illness (X2, an index), and anxiety level (X3, an 
index). The administrator randomly selected 23 patients and 
collected the data presented below, where larger values of Y, X2, 
and X3 are, respectively, associated with more satisfaction, 
increased severity of illness, and more anxiety.

a Prepare a stem-and-leaf plot for each of the predictor 
variables. Are any noteworthy features revealed by these plots?

b Obtain the scatter plot matrix and the correlation matrix. 
Interpret these and state your principal findings.

c Fit regression model (6.5) for three predictor variables to the 
data and state the   estimated regression function. How is b2 
interpreted here?

d Obtain the residuals and prepare a box plot of the residuals. Do 
there appear to be any outliers?

e Plot the residuals against Yhat, each of the predictor variables, 
and each two-factor   interaction term on separate graphs. Also 
prepare a normal probability plot. Interpret your plots and 
summarize your findings.

f Can you conduct a formal test for lack of fit here?

g Conduct the Breusch-Pagan test for constancy of the error 
variance, assuming  log s2i = g0 + g1Xil + g2Xi2 + g3Xi3; use a 
= 0.01. State the alternatives, decision rule, and conclusion.

6.16. Refer to Patient satisfaction Problem 6.15. Assume that 
regression model (6.5) for three predictor variables with 
independent normal error terms is appropriate.

a Test whether there is a regression relation; use a = .10. State 
the alternatives, decision rule, and conclusion. What does your 
test imply about B1, B2. and B3? What is the P-value of the 
test?
 
c Calculate the coefficient of multiple correlation. What does it 
indicate here?

6.17. Refer to Patient satisfaction Problem 6.15. Assume that 
regression model (6.5) for three predictor variables with 
independent normal error terms is appropriate.

a. Obtain an interval estimate of the mean satisfaction when 
Xl = 35, X2 = 45, and   X3 = 2.2. 
Use a 90 percent confidence coefficient. Interpret 
your confidence interval.

b Obtain a prediction interval for a new patient's satisfaction 
when X l = 35, X 2 = 45, and X 3 = 2.2. Use a 90 percent 
confidence coefficient. Interpret your prediction interval.


Satisfaction  Age   Severity  Anxiety
       Y         X1        X2           X3


      48.0      50.0      51.0         2.3
      57.0      36.0      46.0         2.3
      66.0      40.0      48.0         2.2
      70.0      41.0      44.0         1.8
      89.0      28.0      43.0         1.8
      36.0      49.0      54.0         2.9
      46.0      42.0      50.0         2.2
      54.0      45.0      48.0         2.4
      26.0      52.0      62.0         2.9
      77.0      29.0      50.0         2.1
      89.0      29.0      48.0         2.4
      67.0      43.0      53.0         2.4
      47.0      38.0      55.0         2.2
      51.0      34.0      51.0         2.3
      57.0      53.0      54.0         2.2
      66.0      36.0      49.0         2.0
      79.0      33.0      56.0         2.5
      88.0      29.0      46.0         1.9
      60.0      33.0      49.0         2.1
      49.0      55.0      51.0         2.4
      77.0      29.0      52.0         2.3
      52.0      44.0      58.0         2.9
      60.0      43.0      50.0         2.3